Question: Simplify the expression. $(3q^{3}-3q^{2})(-q^{3}+2q^{2}+6q)$
Solution: First use the distributive property. $ 3 q^3 (- q^3) + 3 q^3 (2 q^2) + 3 q^3 (6 q) - 3 q^2 (- q^3) - 3 q^2 (2 q^2) - 3 q^2 (6 q) $ Simplify. $ - 3q^{6} + 6q^{5} + 18q^{4} + 3q^{5} - 6q^{4} - 18q^{3} $ $-3q^{6}+9q^{5}+12q^{4}-18q^{3}$ Identify like terms. $ {- 3q^{6}} \color{#DF0030} {+ 6q^{5}} {+ 18q^{4}} \color{#DF0030} {+ 3q^{5}} {- 6q^{4}} {- 18q^{3}} $ Add the coefficients. $ { -3q^{6}} \color{#DF0030} {+ 9q^{5}} {+ 12q^{4}} { -18q^{3}} $